Stumped on the dimensions of the logo to be placed on the various DPI screen versions while designing Android App

I am trying to design an android app and feel stumped on the dimensions of the logo to be placed on the various DPI screen versions and other scenarios possible. Please suggest what should be the size of logo per DPI screen. I am using attached image as reference for other design specifications such as icons and bar size.

1. I am trying to create a launcher icon
2. Developer has requested different logo size versions as per the screen DPI.
3. What should be the size of the correct size of the logo max and min to be placed on any screen of the app? Is it completely up to the designer?

Thanks in advance.

There are commonly two ways to target all screen DPIs.

1. Easiest way - Make all images to Extra High or Extra Extra High DPI.

2. Safe way - Make all images for every single DPI.

Now my question is what size should my logo be in order to be able to make Make all images for every single DPI.

Hope this help to understand.